It is believed that the calculations which purported to show that bumblebees cannot fly are based upon a simplified linear treatment of oscillating aerofoils. The method assumes small amplitude oscillations without flow separation. This ignores the effect of dynamic stall, an airflow separation inducing a large vortex above the wing, which briefly produces several times the lift of the aerofoil in regular flight. More sophisticated aerodynamic analysis shows that the bumblebee can fly because its wings encounter dynamic stall in every oscillation cycle.
Another description of a bee's wing function is that the wings work similarly to helicopter blades, "reverse-pitch semirotary helicopter blades".
Bees beat their wings approximate 200 times a second, which is 10-20x as fast as nerve impulses can fire. They achieve this because their thorax muscles don't expand and contract on each nerve firing, but rather vibrate like someone plucking a rubber-band.